The APR is 4%, so the semi-annual interest rate is 2%. If you deposit $10,000 in the bank after every six months, you will have $85,829.69 in the bank at the end of 4 years:

1. After six months you will have $10,000

2. After one year you will have 10,000x1.02+10,000 = $20,200

3. After 1.5 years you will have $20,200x1.02+10,000 = $30,604

4. After 2 years you will have $30,604x1.02+10,000 = $41,216.08

5. After 2.5 years you will have $41,216.08x1.02+10,000 = $52,040.40

6. After 3 years you will have $52,040.40x1.02+10,000 = $63,081.21

7. After 3.5 years you will have $63,081.21x1.02+10,000 = $74,342.83

8. After 4 years you will have $74,342.83x1.02+10,000 = $85,829.69

The present value of that $85,829.69, discounting at 2% is $73,254.81 (i.e. $85,829.69/(1.02^8)), so if you put this amount in the bank now, and make the payments every six months, there will be nothing left in the account after four years.